The Joys Of Minimalism

Algebra Level 5

$\large f_a(x,y)=ax^2+4ay^2+20xy+3x+6y+7$

Find the smallest value of the parameter $$a$$ such that $$f_a(x,y)$$ attains a global minimum.

Enter 666 if you come to the conclusion that no such smallest value of $$a$$ exists.

This problem was commissioned by Comrade Pi Han Goh.
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